After a quick Google search my suspicions were confirmed and it would be impossible for any party to win most elections in the US without winning car-owners. Based on the articles I quickly skimmed it seems like somewhere between 85-95% of Americans own cars.
Democrats probably do win the non-drivers handily though.
It's very plausible if the Democrats are winning by huge margins among non-drivers, which they probably are since non-drivers are very heavily urban and/or poor minorities so I would guess non-drivers approach 75-80% Democratic in a neutral environment. So in 51D-49R race it is plausible that Republicans are winning drivers while Democrats are winning overall. But I agree that there's not much room for there to be a distinction between drivers and the overall result.